///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// Restrictions:
///		By making use of the Software for military purposes, you choose to make
///		a Bunny unhappy.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtc_quaternion
/// @file glm/gtc/quaternion.inl
/// @date 2009-05-21 / 2011-06-15
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

#include "../trigonometric.hpp"
#include "../geometric.hpp"
#include "../exponential.hpp"
#include <limits>

namespace glm {
    namespace detail {
        template<typename T, precision P>
        struct compute_dot<tquat, T, P> {
            static GLM_FUNC_QUALIFIER T call(tquat<T, P> const &x, tquat<T, P> const &y) {
                tvec4<T, P> tmp(x.x * y.x, x.y * y.y, x.z * y.z, x.w * y.w);
                return (tmp.x + tmp.y) + (tmp.z + tmp.w);
            }
        };
    }//namespace detail

    //////////////////////////////////////
    // Component accesses

#	ifdef GLM_FORCE_SIZE_FUNC
    template <typename T, precision P>
    GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::size_type tquat<T, P>::size() const
    {
        return 4;
    }

    template <typename T, precision P>
    GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::size_type i)
    {
        assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
        return (&x)[i];
    }

    template <typename T, precision P>
    GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::size_type i) const
    {
        assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
        return (&x)[i];
    }
#	else

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::length_type tquat<T, P>::length() const {
        return 4;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER T &tquat<T, P>::operator[](typename tquat<T, P>::length_type i) {
        assert(i >= 0 &&
               static_cast<detail::component_count_t>(i) < detail::component_count(*this));
        return (&x)[i];
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER T const &tquat<T, P>::operator[](typename tquat<T, P>::length_type i) const {
        assert(i >= 0 &&
               static_cast<detail::component_count_t>(i) < detail::component_count(*this));
        return (&x)[i];
    }

#	endif//GLM_FORCE_SIZE_FUNC

    //////////////////////////////////////
    // Implicit basic constructors

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat()
#		ifndef GLM_FORCE_NO_CTOR_INIT
            : x(0), y(0), z(0), w(1)
#		endif
    {}

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<T, P> const &q)
            : x(q.x), y(q.y), z(q.z), w(q.w) {}

    template<typename T, precision P>
    template<precision Q>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<T, Q> const &q)
            : x(q.x), y(q.y), z(q.z), w(q.w) {}

    //////////////////////////////////////
    // Explicit basic constructors

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(ctor) {}

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(T const &s, tvec3<T, P> const &v)
            : x(v.x), y(v.y), z(v.z), w(s) {}

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(T const &w, T const &x, T const &y, T const &z)
            : x(x), y(y), z(z), w(w) {}

    //////////////////////////////////////////////////////////////
    // Conversions

    template<typename T, precision P>
    template<typename U, precision Q>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<U, Q> const &q)
            : x(static_cast<T>(q.x)), y(static_cast<T>(q.y)), z(static_cast<T>(q.z)),
              w(static_cast<T>(q.w)) {}

    //template <typename valType>
    //GLM_FUNC_QUALIFIER tquat<valType>::tquat
    //(
    //	valType const & pitch,
    //	valType const & yaw,
    //	valType const & roll
    //)
    //{
    //	tvec3<valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5));
    //	tvec3<valType> c = glm::cos(eulerAngle * valType(0.5));
    //	tvec3<valType> s = glm::sin(eulerAngle * valType(0.5));
    //
    //	this->w = c.x * c.y * c.z + s.x * s.y * s.z;
    //	this->x = s.x * c.y * c.z - c.x * s.y * s.z;
    //	this->y = c.x * s.y * c.z + s.x * c.y * s.z;
    //	this->z = c.x * c.y * s.z - s.x * s.y * c.z;
    //}

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const &u, tvec3<T, P> const &v) {
        tvec3<T, P> const LocalW(cross(u, v));
        T Dot = detail::compute_dot<tvec3, T, P>::call(u, v);
        tquat<T, P> q(T(1) + Dot, LocalW.x, LocalW.y, LocalW.z);

        *this = normalize(q);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const &eulerAngle) {
        tvec3<T, P> c = glm::cos(eulerAngle * T(0.5));
        tvec3<T, P> s = glm::sin(eulerAngle * T(0.5));

        this->w = c.x * c.y * c.z + s.x * s.y * s.z;
        this->x = s.x * c.y * c.z - c.x * s.y * s.z;
        this->y = c.x * s.y * c.z + s.x * c.y * s.z;
        this->z = c.x * c.y * s.z - s.x * s.y * c.z;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat3x3<T, P> const &m) {
        *this = quat_cast(m);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat4x4<T, P> const &m) {
        *this = quat_cast(m);
    }

#	if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
    template <typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat3x3<T, P>()
    {
        return mat3_cast(*this);
    }

    template <typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat4x4<T, P>()
    {
        return mat4_cast(*this);
    }
#	endif//GLM_HAS_EXPLICIT_CONVERSION_OPERATORS

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> conjugate(tquat<T, P> const &q) {
        return tquat<T, P>(q.w, -q.x, -q.y, -q.z);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> inverse(tquat<T, P> const &q) {
        return conjugate(q) / dot(q, q);
    }

    //////////////////////////////////////////////////////////////
    // tquat<valType> operators

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> &tquat<T, P>::operator=(tquat<T, P> const &q) {
        this->w = q.w;
        this->x = q.x;
        this->y = q.y;
        this->z = q.z;
        return *this;
    }

    template<typename T, precision P>
    template<typename U>
    GLM_FUNC_QUALIFIER tquat<T, P> &tquat<T, P>::operator=(tquat<U, P> const &q) {
        this->w = static_cast<T>(q.w);
        this->x = static_cast<T>(q.x);
        this->y = static_cast<T>(q.y);
        this->z = static_cast<T>(q.z);
        return *this;
    }

    template<typename T, precision P>
    template<typename U>
    GLM_FUNC_QUALIFIER tquat<T, P> &tquat<T, P>::operator+=(tquat<U, P> const &q) {
        this->w += static_cast<T>(q.w);
        this->x += static_cast<T>(q.x);
        this->y += static_cast<T>(q.y);
        this->z += static_cast<T>(q.z);
        return *this;
    }

    template<typename T, precision P>
    template<typename U>
    GLM_FUNC_QUALIFIER tquat<T, P> &tquat<T, P>::operator*=(tquat<U, P> const &r) {
        tquat<T, P> const p(*this);
        tquat<T, P> const q(r);

        this->w = p.w * q.w - p.x * q.x - p.y * q.y - p.z * q.z;
        this->x = p.w * q.x + p.x * q.w + p.y * q.z - p.z * q.y;
        this->y = p.w * q.y + p.y * q.w + p.z * q.x - p.x * q.z;
        this->z = p.w * q.z + p.z * q.w + p.x * q.y - p.y * q.x;
        return *this;
    }

    template<typename T, precision P>
    template<typename U>
    GLM_FUNC_QUALIFIER tquat<T, P> &tquat<T, P>::operator*=(U s) {
        this->w *= static_cast<U>(s);
        this->x *= static_cast<U>(s);
        this->y *= static_cast<U>(s);
        this->z *= static_cast<U>(s);
        return *this;
    }

    template<typename T, precision P>
    template<typename U>
    GLM_FUNC_QUALIFIER tquat<T, P> &tquat<T, P>::operator/=(U s) {
        this->w /= static_cast<U>(s);
        this->x /= static_cast<U>(s);
        this->y /= static_cast<U>(s);
        this->z /= static_cast<U>(s);
        return *this;
    }

    //////////////////////////////////////////////////////////////
    // tquat<T, P> external operators

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> operator-(tquat<T, P> const &q) {
        return tquat<T, P>(-q.w, -q.x, -q.y, -q.z);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> operator+(tquat<T, P> const &q, tquat<T, P> const &p) {
        return tquat<T, P>(q) += p;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const &q, tquat<T, P> const &p) {
        return tquat<T, P>(q) *= p;
    }

    // Transformation
    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tquat<T, P> const &q, tvec3<T, P> const &v) {
        tvec3<T, P> const QuatVector(q.x, q.y, q.z);
        tvec3<T, P> const uv(glm::cross(QuatVector, v));
        tvec3<T, P> const uuv(glm::cross(QuatVector, uv));

        return v + ((uv * q.w) + uuv) * static_cast<T>(2);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tvec3<T, P> const &v, tquat<T, P> const &q) {
        return glm::inverse(q) * v;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tquat<T, P> const &q, tvec4<T, P> const &v) {
        return tvec4<T, P>(q * tvec3<T, P>(v), v.w);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tvec4<T, P> const &v, tquat<T, P> const &q) {
        return glm::inverse(q) * v;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const &q, T const &s) {
        return tquat<T, P>(
                q.w * s, q.x * s, q.y * s, q.z * s);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> operator*(T const &s, tquat<T, P> const &q) {
        return q * s;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> operator/(tquat<T, P> const &q, T const &s) {
        return tquat<T, P>(
                q.w / s, q.x / s, q.y / s, q.z / s);
    }

    //////////////////////////////////////
    // Boolean operators

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER bool operator==(tquat<T, P> const &q1, tquat<T, P> const &q2) {
        return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER bool operator!=(tquat<T, P> const &q1, tquat<T, P> const &q2) {
        return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w);
    }

    ////////////////////////////////////////////////////////
    template<typename T, precision P>
    GLM_FUNC_QUALIFIER T length(tquat<T, P> const &q) {
        return glm::sqrt(dot(q, q));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> normalize(tquat<T, P> const &q) {
        T len = length(q);
        if (len <= T(0)) // Problem
            return tquat<T, P>(1, 0, 0, 0);
        T oneOverLen = T(1) / len;
        return tquat<T, P>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> cross(tquat<T, P> const &q1, tquat<T, P> const &q2) {
        return tquat<T, P>(
                q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z,
                q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y,
                q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z,
                q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x);
    }

/*
	// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle))
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> const & y, T const & a)
	{
		if(a <= T(0)) return x;
		if(a >= T(1)) return y;

		float fCos = dot(x, y);
		tquat<T, P> y2(y); //BUG!!! tquat<T, P> y2;
		if(fCos < T(0))
		{
			y2 = -y;
			fCos = -fCos;
		}

		//if(fCos > 1.0f) // problem
		float k0, k1;
		if(fCos > T(0.9999))
		{
			k0 = T(1) - a;
			k1 = T(0) + a; //BUG!!! 1.0f + a;
		}
		else
		{
			T fSin = sqrt(T(1) - fCos * fCos);
			T fAngle = atan(fSin, fCos);
			T fOneOverSin = static_cast<T>(1) / fSin;
			k0 = sin((T(1) - a) * fAngle) * fOneOverSin;
			k1 = sin((T(0) + a) * fAngle) * fOneOverSin;
		}

		return tquat<T, P>(
			k0 * x.w + k1 * y2.w,
			k0 * x.x + k1 * y2.x,
			k0 * x.y + k1 * y2.y,
			k0 * x.z + k1 * y2.z);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> mix2
	(
		tquat<T, P> const & x, 
		tquat<T, P> const & y, 
		T const & a
	)
	{
		bool flip = false;
		if(a <= static_cast<T>(0)) return x;
		if(a >= static_cast<T>(1)) return y;

		T cos_t = dot(x, y);
		if(cos_t < T(0))
		{
			cos_t = -cos_t;
			flip = true;
		}

		T alpha(0), beta(0);

		if(T(1) - cos_t < 1e-7)
			beta = static_cast<T>(1) - alpha;
		else
		{
			T theta = acos(cos_t);
			T sin_t = sin(theta);
			beta = sin(theta * (T(1) - alpha)) / sin_t;
			alpha = sin(alpha * theta) / sin_t;
		}

		if(flip)
			alpha = -alpha;
		
		return normalize(beta * x + alpha * y);
	}
*/

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> mix(tquat<T, P> const &x, tquat<T, P> const &y, T a) {
        T cosTheta = dot(x, y);

        // Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
        if (cosTheta > T(1) - epsilon<T>()) {
            // Linear interpolation
            return tquat<T, P>(
                    mix(x.w, y.w, a),
                    mix(x.x, y.x, a),
                    mix(x.y, y.y, a),
                    mix(x.z, y.z, a));
        } else {
            // Essential Mathematics, page 467
            T angle = acos(cosTheta);
            return (sin((T(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle);
        }
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> lerp(tquat<T, P> const &x, tquat<T, P> const &y, T a) {
        // Lerp is only defined in [0, 1]
        assert(a >= static_cast<T>(0));
        assert(a <= static_cast<T>(1));

        return x * (T(1) - a) + (y * a);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> slerp(tquat<T, P> const &x, tquat<T, P> const &y, T a) {
        tquat<T, P> z = y;

        T cosTheta = dot(x, y);

        // If cosTheta < 0, the interpolation will take the long way around the sphere.
        // To fix this, one quat must be negated.
        if (cosTheta < T(0)) {
            z = -y;
            cosTheta = -cosTheta;
        }

        // Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
        if (cosTheta > T(1) - epsilon<T>()) {
            // Linear interpolation
            return tquat<T, P>(
                    mix(x.w, z.w, a),
                    mix(x.x, z.x, a),
                    mix(x.y, z.y, a),
                    mix(x.z, z.z, a));
        } else {
            // Essential Mathematics, page 467
            T angle = acos(cosTheta);
            return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle);
        }
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P>
    rotate(tquat<T, P> const &q, T const &angle, tvec3<T, P> const &v) {
        tvec3<T, P> Tmp = v;

        // Axis of rotation must be normalised
        T len = glm::length(Tmp);
        if (abs(len - T(1)) > T(0.001)) {
            T oneOverLen = static_cast<T>(1) / len;
            Tmp.x *= oneOverLen;
            Tmp.y *= oneOverLen;
            Tmp.z *= oneOverLen;
        }

        T const AngleRad(angle);
        T const Sin = sin(AngleRad * T(0.5));

        return q * tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
        //return gtc::quaternion::cross(q, tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec3<T, P> eulerAngles(tquat<T, P> const &x) {
        return tvec3<T, P>(pitch(x), yaw(x), roll(x));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER T roll(tquat<T, P> const &q) {
        return T(atan(T(2) * (q.x * q.y + q.w * q.z),
                      q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER T pitch(tquat<T, P> const &q) {
        return T(atan(T(2) * (q.y * q.z + q.w * q.x),
                      q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER T yaw(tquat<T, P> const &q) {
        return asin(T(-2) * (q.x * q.z - q.w * q.y));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tmat3x3<T, P> mat3_cast(tquat<T, P> const &q) {
        tmat3x3<T, P> Result(T(1));
        T qxx(q.x * q.x);
        T qyy(q.y * q.y);
        T qzz(q.z * q.z);
        T qxz(q.x * q.z);
        T qxy(q.x * q.y);
        T qyz(q.y * q.z);
        T qwx(q.w * q.x);
        T qwy(q.w * q.y);
        T qwz(q.w * q.z);

        Result[0][0] = 1 - 2 * (qyy + qzz);
        Result[0][1] = 2 * (qxy + qwz);
        Result[0][2] = 2 * (qxz - qwy);

        Result[1][0] = 2 * (qxy - qwz);
        Result[1][1] = 1 - 2 * (qxx + qzz);
        Result[1][2] = 2 * (qyz + qwx);

        Result[2][0] = 2 * (qxz + qwy);
        Result[2][1] = 2 * (qyz - qwx);
        Result[2][2] = 1 - 2 * (qxx + qyy);
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tmat4x4<T, P> mat4_cast(tquat<T, P> const &q) {
        return tmat4x4<T, P>(mat3_cast(q));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(tmat3x3<T, P> const &m) {
        T fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2];
        T fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2];
        T fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1];
        T fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2];

        int biggestIndex = 0;
        T fourBiggestSquaredMinus1 = fourWSquaredMinus1;
        if (fourXSquaredMinus1 > fourBiggestSquaredMinus1) {
            fourBiggestSquaredMinus1 = fourXSquaredMinus1;
            biggestIndex = 1;
        }
        if (fourYSquaredMinus1 > fourBiggestSquaredMinus1) {
            fourBiggestSquaredMinus1 = fourYSquaredMinus1;
            biggestIndex = 2;
        }
        if (fourZSquaredMinus1 > fourBiggestSquaredMinus1) {
            fourBiggestSquaredMinus1 = fourZSquaredMinus1;
            biggestIndex = 3;
        }

        T biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5);
        T mult = static_cast<T>(0.25) / biggestVal;

        tquat<T, P> Result(uninitialize);
        switch (biggestIndex) {
            case 0:
                Result.w = biggestVal;
                Result.x = (m[1][2] - m[2][1]) * mult;
                Result.y = (m[2][0] - m[0][2]) * mult;
                Result.z = (m[0][1] - m[1][0]) * mult;
                break;
            case 1:
                Result.w = (m[1][2] - m[2][1]) * mult;
                Result.x = biggestVal;
                Result.y = (m[0][1] + m[1][0]) * mult;
                Result.z = (m[2][0] + m[0][2]) * mult;
                break;
            case 2:
                Result.w = (m[2][0] - m[0][2]) * mult;
                Result.x = (m[0][1] + m[1][0]) * mult;
                Result.y = biggestVal;
                Result.z = (m[1][2] + m[2][1]) * mult;
                break;
            case 3:
                Result.w = (m[0][1] - m[1][0]) * mult;
                Result.x = (m[2][0] + m[0][2]) * mult;
                Result.y = (m[1][2] + m[2][1]) * mult;
                Result.z = biggestVal;
                break;

            default:                    // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity.
                assert(false);
                break;
        }
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(tmat4x4<T, P> const &m4) {
        return quat_cast(tmat3x3<T, P>(m4));
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER T angle(tquat<T, P> const &x) {
        return acos(x.w) * T(2);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec3<T, P> axis(tquat<T, P> const &x) {
        T tmp1 = static_cast<T>(1) - x.w * x.w;
        if (tmp1 <= static_cast<T>(0))
            return tvec3<T, P>(0, 0, 1);
        T tmp2 = static_cast<T>(1) / sqrt(tmp1);
        return tvec3<T, P>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tquat<T, P> angleAxis(T const &angle, tvec3<T, P> const &v) {
        tquat<T, P> Result(uninitialize);

        T const a(angle);
        T const s = glm::sin(a * static_cast<T>(0.5));

        Result.w = glm::cos(a * static_cast<T>(0.5));
        Result.x = v.x * s;
        Result.y = v.y * s;
        Result.z = v.z * s;
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<bool, P> lessThan(tquat<T, P> const &x, tquat<T, P> const &y) {
        tvec4<bool, P> Result(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(x); ++i)
            Result[i] = x[i] < y[i];
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<bool, P> lessThanEqual(tquat<T, P> const &x, tquat<T, P> const &y) {
        tvec4<bool, P> Result(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(x); ++i)
            Result[i] = x[i] <= y[i];
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThan(tquat<T, P> const &x, tquat<T, P> const &y) {
        tvec4<bool, P> Result(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(x); ++i)
            Result[i] = x[i] > y[i];
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThanEqual(tquat<T, P> const &x, tquat<T, P> const &y) {
        tvec4<bool, P> Result(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(x); ++i)
            Result[i] = x[i] >= y[i];
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<bool, P> equal(tquat<T, P> const &x, tquat<T, P> const &y) {
        tvec4<bool, P> Result(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(x); ++i)
            Result[i] = x[i] == y[i];
        return Result;
    }

    template<typename T, precision P>
    GLM_FUNC_QUALIFIER tvec4<bool, P> notEqual(tquat<T, P> const &x, tquat<T, P> const &y) {
        tvec4<bool, P> Result(uninitialize);
        for (detail::component_count_t i = 0; i < detail::component_count(x); ++i)
            Result[i] = x[i] != y[i];
        return Result;
    }
}//namespace glm
